結果

問題 No.2764 Warp Drive Spacecraft
ユーザー dyktr_06dyktr_06
提出日時 2024-05-18 01:20:28
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 565 ms / 3,000 ms
コード長 8,628 bytes
コンパイル時間 3,041 ms
コンパイル使用メモリ 225,728 KB
実行使用メモリ 48,444 KB
最終ジャッジ日時 2024-05-18 01:20:43
合計ジャッジ時間 13,642 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,816 KB
testcase_01 AC 2 ms
6,940 KB
testcase_02 AC 2 ms
6,940 KB
testcase_03 AC 3 ms
6,944 KB
testcase_04 AC 2 ms
6,940 KB
testcase_05 AC 3 ms
6,948 KB
testcase_06 AC 3 ms
6,944 KB
testcase_07 AC 2 ms
6,940 KB
testcase_08 AC 3 ms
6,940 KB
testcase_09 AC 2 ms
6,940 KB
testcase_10 AC 2 ms
6,940 KB
testcase_11 AC 2 ms
6,944 KB
testcase_12 AC 3 ms
6,940 KB
testcase_13 AC 3 ms
6,940 KB
testcase_14 AC 2 ms
6,940 KB
testcase_15 AC 2 ms
6,940 KB
testcase_16 AC 205 ms
45,396 KB
testcase_17 AC 171 ms
45,268 KB
testcase_18 AC 173 ms
46,036 KB
testcase_19 AC 394 ms
34,620 KB
testcase_20 AC 524 ms
34,880 KB
testcase_21 AC 400 ms
34,896 KB
testcase_22 AC 406 ms
38,088 KB
testcase_23 AC 427 ms
34,716 KB
testcase_24 AC 402 ms
37,240 KB
testcase_25 AC 385 ms
34,960 KB
testcase_26 AC 550 ms
47,420 KB
testcase_27 AC 526 ms
46,036 KB
testcase_28 AC 554 ms
46,256 KB
testcase_29 AC 539 ms
46,720 KB
testcase_30 AC 512 ms
46,764 KB
testcase_31 AC 565 ms
47,452 KB
testcase_32 AC 557 ms
48,444 KB
testcase_33 AC 185 ms
26,284 KB
testcase_34 AC 178 ms
26,320 KB
testcase_35 AC 176 ms
26,312 KB
testcase_36 AC 181 ms
39,296 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;

#define overload4(_1, _2, _3, _4, name, ...) name
#define rep1(n) for(int i = 0; i < (int)(n); ++i)
#define rep2(i, n) for(int i = 0; i < (int)(n); ++i)
#define rep3(i, a, b) for(int i = (a); i < (int)(b); ++i)
#define rep4(i, a, b, c) for(int i = (a); i < (int)(b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; --i)
#define ALL(a) (a).begin(), (a).end()
#define Sort(a) (sort((a).begin(), (a).end()))
#define RSort(a) (sort((a).rbegin(), (a).rend()))
#define UNIQUE(a) (a.erase(unique((a).begin(), (a).end()), (a).end()))

typedef long long int ll;
typedef unsigned long long ul;
typedef long double ld;
typedef vector<int> vi;
typedef vector<long long> vll;
typedef vector<char> vc;
typedef vector<string> vst;
typedef vector<double> vd;
typedef vector<long double> vld;
typedef pair<long long, long long> P;

template<class T> long long sum(const T& a){ return accumulate(a.begin(), a.end(), 0LL); }
template<class T> auto min(const T& a){ return *min_element(a.begin(), a.end()); }
template<class T> auto max(const T& a){ return *max_element(a.begin(), a.end()); }

const long long MINF = 0x7fffffffffff;
const long long INF = 0x1fffffffffffffff;
const long long MOD = 998244353;
const long double EPS = 1e-9;
const long double PI = acos(-1);

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

template<typename T1, typename T2> istream &operator>>(istream &is, pair<T1, T2> &p){ is >> p.first >> p.second; return is; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){ os << "(" << p.first << ", " << p.second << ")"; return os; }
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for(T &in : v) is >> in; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &v){ for(int i = 0; i < (int) v.size(); ++i){ os << v[i] << (i + 1 != (int) v.size() ? " " : ""); } return os; }
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp){ for(auto &[key, val] : mp){ os << key << ":" << val << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, queue<T> q){ while(q.size()){ os << q.front() << " "; q.pop(); } return os; }
template <typename T> ostream &operator<<(ostream &os, deque<T> q){ while(q.size()){ os << q.front() << " "; q.pop_front(); } return os; }
template <typename T> ostream &operator<<(ostream &os, stack<T> st){ while(st.size()){ os << st.top() << " "; st.pop(); } return os; }
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq){ while(pq.size()){ os << pq.top() << " "; pq.pop(); } return os; }

template<class T, class U> inline T vin(T& vec, U n) { vec.resize(n); for(int i = 0; i < (int) n; ++i) cin >> vec[i]; return vec; }
template<class T> inline void vout(T vec, string s = "\n"){ for(auto x : vec) cout << x << s; }
template<class... T> void in(T&... a){ (cin >> ... >> a); }
void out(){ cout << '\n'; }
template<class T, class... Ts> void out(const T& a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; }
template<class T, class U> void inGraph(vector<vector<T>>& G, U n, U m, bool directed = false){ G.resize(n); for(int i = 0; i < m; ++i){ int a, b; cin >> a >> b; a--, b--; G[a].push_back(b); if(!directed) G[b].push_back(a); } }

template<typename T, T x_low, T x_high, T id>
struct DynamicLiChaoTree{
    struct Line{
        T a, b;

        Line(T _a, T _b) : a(_a), b(_b) {}

        inline T get(T x) const {
            return a * x + b;
        }
    };

    struct Node{
        Line x;
        Node *l, *r;

        Node(const Line &x) : x{x}, l{nullptr}, r{nullptr} {}
    };

    Node *root = nullptr;

    DynamicLiChaoTree() {}

private:
    Node *add_line_(Node *t, Line &x, const T &l, const T &r, const T &x_l, const T &x_r){
        if(!t){
            return new Node(x);
        }

        T t_l = t->x.get(l), t_r = t->x.get(r);

        if(t_l <= x_l && t_r <= x_r){
            return t;
        } else if(t_l >= x_l && t_r >= x_r){
            t->x = x;
            return t;
        } else{
            T m = (l + r) / 2;
            if(m == r) --m;
            T t_m = t->x.get(m), x_m = x.get(m);
            if(t_m > x_m){
                swap(t->x, x);
                if(t_l <= x_l){
                    t->l = add_line_(t->l, x, l, m, t_l, t_m);
                } else{
                    t->r = add_line_(t->r, x, m + 1, r, t_m + x.a, t_r);
                }
            } else{
                if(x_l <= t_l){
                    t->l = add_line_(t->l, x, l, m, x_l, x_m);
                } else{
                    t->r = add_line_(t->r, x, m + 1, r, x_m + x.a, x_r);
                }
            }
            return t;
        }
    }

    Node *add_segment_(Node *t, Line &x, const T &a, const T &b, const T &l, const T &r, const T &x_l, const T &x_r){
        if(r < a || b < l) return t;
        if(a <= l && r <= b){
            Line y{x};
            return add_line_(t, y, l, r, x_l, x_r);
        }
        if(t){
            T t_l = t->x.get(l), t_r = t->x.get(r);
            if(t_l <= x_l && t_r <= x_r) return t;
        } else{
            t = new Node(Line(0, id));
        }

        T m = (l + r) / 2;
        if(m == r) --m;
        T x_m = x.get(m);
        t->l = add_segment_(t->l, x, a, b, l, m, x_l, x_m);
        t->r = add_segment_(t->r, x, a, b, m + 1, r, x_m + x.a, x_r);
        return t;
    }

    T query_(const Node *t, const T &l, const T &r, const T &x_c) const {
        if(!t) return id;
        if(l == r) return t->x.get(x_c);
        T m = (l + r) / 2;
        if(m == r) --m;
        if(x_c <= m){
            return min(t->x.get(x_c), query_(t->l, l, m, x_c));
        } else{
            return min(t->x.get(x_c), query_(t->r, m + 1, r, x_c));
        }
    }

public:
    void add_line(const T &a, const T &b){
        Line x(a, b);
        root = add_line_(root, x, x_low, x_high, x.get(x_low), x.get(x_high));
    }

    void add_segment(const T &l, const T &r, const T &a, const T &b){
        Line x(a, b);
        root = add_segment_(root, x, l, r - 1, x_low, x_high, x.get(x_low), x.get(x_high));
    }

    T query(const T &x) const {
        return query_(root, x_low, x_high, x);
    }
};

void input(){
}

void solve(){
    ll n, m; in(n, m);
    vll w; vin(w, n);
    vector<vector<array<ll, 2>>> G(n * 2);
    rep(i, m){
        ll u, v, t; in(u, v, t);
        u--, v--;
        G[u].push_back({v, t});
        G[u + n].push_back({v + n, t});
        G[v].push_back({u, t});
        G[v + n].push_back({u + n, t});
    }

    vector<P> p(n);
    rep(i, n) p[i] = {w[i], i};
    Sort(p);
    DynamicLiChaoTree<ll, -2000000000LL, 2000000000LL, INF> lct;

    vll cost(n * 2, INF);
    cost[0] = 0;
    priority_queue<P, vector<P>, greater<P>> pq;
    pq.push({0, 0});

    ll curr = 0;
    while(pq.size() || curr < n){
        if(pq.empty()){
            auto [wi, idx] = p[curr];
            idx += n;
            if(chmin(cost[idx], lct.query(wi))){
                pq.emplace(cost[idx], idx);
            }
            curr++;
            continue;
        }

        auto [c, v] = pq.top();
        if(curr < n){
            auto [wi, idx] = p[curr];
            idx += n;
            ll c2 = lct.query(wi);
            if(c2 <= c){
                curr++;
                if(chmin(cost[idx], c2)){
                    pq.emplace(cost[idx], idx);
                    continue;
                }
            }
        }

        pq.pop();
        if(v < n) lct.add_line(w[v], cost[v]);
        if(cost[v] < c) continue;
        for(auto [nv, t] : G[v]){
            if(chmin(cost[nv], c + t)){
                pq.push({cost[nv], nv});
            }
        }
    }
    out(min(cost[n - 1], cost[n * 2 - 1]));
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(20);

    input();
    solve();
}
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